The present invention relates to a new and distinct strawberry cultivar designated ‘DrisStrawSix’ and botanically known as Fragaria×ananassa. This new strawberry cultivar was discovered in Hillsborough, Fla. in December, 2002 and originated from a cross between the female proprietary parent ‘74G14’ (unpatented) and the male proprietary parent ‘6F-158’ (unpatented). The original seedling of the new cultivar was asexually propagated at a nursery in Shasta County, Calif. ‘DrisStrawSix’ was subsequently asexually propagated and underwent further testing at a nursery in Hillsborough, Fla. for five years. The present invention has been found to retain its distinctive characteristics through successive asexual propagations.